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Displaying similar documents to “The localisation of primes in arithmetic progressions of irrational modulus”

Primes in tuples IV: Density of small gaps between consecutive primes

Daniel Alan Goldston, János Pintz, Cem Yalçın Yıldırım (2013)

Acta Arithmetica

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We prove that given any small but fixed η > 0, a positive proportion of all gaps between consecutive primes are smaller than η times the average gap. We show some unconditional and conditional quantitative results in this vein. In the results the dependence on η is given explicitly, providing a new quantitative way, in addition to that of the first paper in this series, of measuring the effect of the knowledge on the level of distribution of primes.

Gaps between primes in Beatty sequences

Roger C. Baker, Liangyi Zhao (2016)

Acta Arithmetica

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We study the gaps between primes in Beatty sequences following the methods in the recent breakthrough by Maynard (2015).

Levels of Distribution and the Affine Sieve

Alex Kontorovich (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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We discuss the notion of a “Level of Distribution” in two settings. The first deals with primes in progressions, and the role this plays in Yitang Zhang’s theorem on bounded gaps between primes. The second concerns the Affine Sieve and its applications.

Topological aspects of infinitude of primes in arithmetic progressions

František Marko, Štefan Porubský (2015)

Colloquium Mathematicae

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We investigate properties of coset topologies on commutative domains with an identity, in particular, the 𝓢-coprime topologies defined by Marko and Porubský (2012) and akin to the topology defined by Furstenberg (1955) in his proof of the infinitude of rational primes. We extend results about the infinitude of prime or maximal ideals related to the Dirichlet theorem on the infinitude of primes from Knopfmacher and Porubský (1997), and correct some results from that paper. Then we determine...